This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another...

A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

In this paper, we propose a novel entropy-based resampling scheme valid for non-stationary data. In particular, we identify the reason for the failure of the original entropy-based algorithm of Vinod and Lopez-de Lacalle (2009) to be the perfect rank correlation between the actual and...

Extensive research has been conducted on the properties of quadratic forms in normal random variables, represented by the symbol Q here. However, analytical results on the square root of the quadratic form, √Q, are limited. The square root of the quadratic form is, for example, used in finance...

The upper tail of the firm size distribution is often assumed to follows a Power Law behavior. Recently, using different estimators and on different data sets, several papers conclude that this distribution follows the Zipf Law, that is that the fraction of firms whose size is above a given...

This paper examines the understanding of business concentration through the Herfindahl- Hirschman Index (HHI), by showing that this index is conceptually a model according to which this concentration is the consequence of a renewal process. This process is prompted by firms engaging in different...

We present a new Monte-Carlo methodology to forecast the crude oil production of Norway and the U.K. based on a two-step process, (i) the nonlinear extrapolation of the current/past performances of individual oil fields and (ii) a stochastic model of the frequency of future oil field...

It has been found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes. This paper introduces a simple method which guarantees convergence of this t-statistic to a...